# Current induced by permanent magnet moving along toroid coil

(It's not really shown in the pictures, but please assume that the coils are included in a closed circuit in both configurations. Maybe they could serve as a tension source in their respective circuit ?)

When a permanent magnet moving on a circular path passes close to a coil periodically (see figure above), it induces an AC in the circuit (I think, correct me if I'm wrong).

I was wondering : if a permanent magnet moves in a circular path, but this time along the side of a toroid, what happens ? Based on my intuition alone, i'd say that it induces a (relatively) direct current. Is it correct ? If so, can we put that into equations ? I'm a bit shaky with Faraday's law, so I don't really know how to do it.

This is not a homework question. As such, I have not included any factors (Speed of magnet, radius, number of loops...) because we can just make them up as we go. If we need to know a factor, then let's just add it in.

Also, please feel free to suggest variations of the problem if they seem interesting, like changing the path of the magnet or whatever.

In the first image as the magnet moves from the six o'clock position to the twelve o'clock position, the magnetic flux through the coil changes (it increases).

By Faraday's law: $$EMF = -\frac{\Delta \Phi}{\Delta t}$$. As flux through the coil changes over time, EMF is generated. As the magnet retreats, the flux decreases, and the reverse EMF is generated. Net result: alternating current.

In the second image, the six o'clock and twelve o'clock positions are symmetrically identical. The total flux in the coil is the same. As the total flux is not changing over time, there is no EMF generated (and therefore no current)

• Thanks for your answer ! When you say "passes through the coil", what area are you considering ? The area formed by a loop in the coil ? Jan 22 '19 at 22:55
• Yes. The specifics don't matter, just that there is some change in the flux. hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html. The important bit is that #2 is symmetric and #1 is not. That changes the behavior. Jan 22 '19 at 23:11
• Ok, thanks. So I take it there is no way to produce a DC using a moving magnet, since it would have to get farther then closer periodically, and this would induce an AC by Faraday's law ? Jan 22 '19 at 23:21
• You can't do it directly with only a magnet and wire. That would require constantly increasing (or decreasing) flux. Jan 22 '19 at 23:30